Identifier: C4T2L1 | Revision: 2026-10-26 | Planned study: 10–15 minutes, excluding extended practice.

Decision and objectives

Choose whether the method addresses this lesson’s task before placing an order. Objectives: 1. Calculate a small historical volatility estimate. 2. Infer implied volatility from a supplied model table. 3. Explain a premium loss after a favorable underlying move.

Prerequisite: C4T1L5 and the completed earlier classes. Foundation: Stock Market School.

All numbers, quotes, contract terms and dates in the case are hypothetical teaching assumptions, not a listed series or offer. Unless varied below, options are European, expire together in 90 calendar days, are cash settled in TRY, and use 100 underlying units per contract. Premiums are TRY per underlying unit, paid at entry; signed quantities identify long (+) and short (−) legs. Assume no distributions and zero financing for the isolated payoff, no holiday adjustment, and final cash on the next business day. Actual tax is excluded, not assumed zero.

Mechanics

Volatility describes dispersion of returns, not direction. Historical volatility summarizes an observed series with a stated sampling and annualization convention. Implied volatility is the input that makes a specified pricing model match an observed option premium. It belongs to a particular strike, expiry and quotation time. It is neither a guaranteed future realized volatility nor a direct forecast of the underlying price. A stale premium, wrong dividend or wrong exercise model can produce a misleading implied number.

Price and return drivers

Premium changes with underlying, strike, remaining time, implied volatility, rates and distributions. Holding other inputs fixed, a standard long vanilla option generally benefits from increased volatility, but the executable price also includes spread and market conditions. Annualized sample volatility = sample daily standard deviation × square root of assumed trading days. The scaling assumes a stable variance process with sufficiently independent returns; a short event-heavy series does not justify that assumption as a forecast.

Worked case

Four hypothetical simple daily returns are +1%, −1%, +2%, −2%. Mean is zero; squared decimal deviations sum to 0.0010. Dividing by n−1 = 3 gives sample daily variance 0.0003333333. Daily standard deviation is 1.8257%; using 252 trading days yields 28.9828% annualized. Separately, an original model table for a European call with S100, K100, T0.25 years, zero rates and no dividends gives premium 3.9878 at volatility 20%, and 5.9785 at 30%. A supplied midpoint near 5.98 therefore corresponds approximately to 30% in this model, not to the four-return estimate by definition.

Adverse case

A long K100 call purchased at 6 loses TRY 120 after TRY 20 costs if its supplied pre-expiry bid later falls to 5 despite S rising from 100 to 103. The quote incorporates an implied-volatility fall and less remaining time. At expiry S90, S100 and S120 its net results are −620, −620 and +1380. The expiry formula contains no implied volatility because the right is then resolved. Before expiry the same S can support different premiums under different conditional inputs.

Practical use

Record the return window, observation frequency, premium side and pricing model. Implied volatility inferred from a midpoint is not the level implied by a purchase ask.

For any actual domestic implementation, verify the exact issue/contract, authorized intermediary, account permission and executable size. Include spread, commissions, passed-through fees, funding/borrow, custody and exercise/exit costs without double-counting embedded charges. Recheck income year, residency/status, issue/acquisition dates and effective tax law; all case results remain before actual tax.

Decision boundaries

Use a historical estimate to describe the chosen period and a consistent implied surface to price a current scenario. Do not buy a low-priced option solely because a noisy historical estimate exceeds its implied volatility. The horizon, jumps, bid/ask, dividends and model can explain the difference. Decline when the source timestamp or quote side is unavailable. Report the estimation window and whether the premium was a bid, ask, midpoint or execution.

Practice and references

Exercise: daily returns +2%, −2%, +2%, −2%, mean zero. Solution: Squared deviations sum to 0.0016; sample variance is 0.0016/3. Daily standard deviation is 2.3094%; annualization at 252 days gives 36.6606%. This is a calculation on four observations, not credible evidence of a stable annual volatility. Compare it to a matched option input only after documenting its horizon and model.

Takeaway: Historical volatility summarizes chosen observations; implied volatility reconciles a model and a quoted premium. Reference links: product card, formula; glossary: Implied volatility; Historical volatility. Next: C4T2L2. Topic test.

Sources: Borsa Istanbul: Options (retrieved 2026-10-26; General information and basic concepts). Borsa Istanbul: Settlement Method (retrieved 2026-10-26; Settlement by contract family). Options Industry Council: Black-Scholes Formula (retrieved 2026-10-26; Inputs and pricing-model limitations). GIB: Provisional Article67 Guide for Individuals (retrieved 2026-10-26; Sections1,3–9 and19; publication introduction). Revision 2026-10-26; recheck changing terms before publication.

Shared reference guide